Questions tagged [product-states]

Having to do with problems which are primarily concerned with some state, which is a tensor product of states on each of its smallest subsystems, and where this represents a significant restriction on the problem (e.g., if it would be more common to consider an arbitrary state).

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Figuring out which experiment is being performed from the results of the experiment

Consider two different experiments involving qubits. In Experiment 1, a qubit is prepared in the mixed state $I/2$, where $I$ is the $2 × 2$ identity matrix. Alice then chooses an orthonormal basis $B$...
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How to show that the QFT satisfies $\frac1{\sqrt N}\sum_j\prod_le^{2\pi i j_l k/2^l}|j_1...j_n⟩=\bigotimes_l \frac1{\sqrt2}(|0⟩+e^{2\pi i k/2^l}|1⟩)$?

I'm reading Ronald de Wolf's lecture notes, and in chapter 4.5 he writes that $$ \frac{1}{\sqrt N}\sum\limits_{j=0}^{N-1}\prod\limits_{l=1}^{n}e^{2\pi i j_l k / 2^l}|j_1...j_n\rangle = \bigotimes\...
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For bipartite mixed state, if one part is pure, then the global mixed state is a product state?

In Nielsen and Chuang, the chapter about Schmidt decomposition, there is an interesting result states that for a bipartite pure state $|\psi\rangle_{AB}$, if part A is a pure state, then $|\psi\...
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Is factoring of a product state unique?

Suppose I have a product state of two qubits (i.e. a vector of size 4x1). Given it is separable (no entanglement), is this separation unique?